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The multilayer network framework has served to describe and uncover a number of novel and unforeseen physical behaviors and regimes in interacting complex systems. However, the majority of existing studies are built on undirected multilayer networks while most complex systems in nature exhibit directed interactions. Here, we propose a framework to analyze diffusive dynamics on multilayer networks consisting of at least one directed layer. We rigorously demonstrate that directionality in multilayer networks can fundamentally change the behavior of diffusive dynamics: from monotonic (in undirected systems) to non-monotonic diffusion with respect to the interlayer coupling strength. Moreover, for certain multilayer network configurations, the directionality can induce a unique superdiffusion regime for intermediate values of the interlayer coupling, wherein the diffusion is even faster than that corresponding to the theoretical limit for undirected systems, i.e. the diffusion in the integrated network obtained from the aggregation of each layer. We theoretically and numerically show that the existence of superdiffusion is fully determined by the directionality of each layer and the topological overlap between layers. We further provide a formulation of multilayer networks displaying superdiffusion. Our results highlight the significance of incorporating the interacting directionality in multilevel networked systems and provide a framework to analyze dynamical processes on interconnected complex systems with directionality.

 

Abstract Understanding the physical drivers of seasonal hydroclimatic variability and improving predictive skill remains a challenge with important socioeconomic and environmental implications for many regions around the world. Physics-based deterministic models show limited ability to predict precipitation as the lead time increases, due to imperfect representation of physical processes and incomplete knowledge of initial conditions. Similarly, statistical methods drawing upon established climate teleconnections have low prediction skill due to the complex nature of the climate system. Recently, promising data-driven approaches have been proposed, but they often suffer from overparameterization and overfitting due to the short observational record, and they often do not account for spatiotemporal dependencies among covariates (i.e., predictors such as sea surface temperatures). This study addresses these challenges via a predictive model based on a graph-guided regularizer that simultaneously promotes similarity of predictive weights for highly correlated covariates and enforces sparsity in the covariate domain. This approach both decreases the effective dimensionality of the problem and identifies the most predictive features without specifying them a priori. We use large ensemble simulations from a climate model to construct this regularizer, reducing the structural uncertainty in the estimation. We apply the learned model to predict winter precipitation in the southwestern United States using sea surface temperatures over the entire Pacific basin, and demonstrate its superiority compared to other regularization approaches and statistical models informed by known teleconnections. Our results highlight the potential to combine optimally the space–time structure of predictor variables learned from climate models with new graph-based regularizers to improve seasonal prediction. 

The knowledge of structural controls of river networks (RNs) on transport dynamics is important for modeling and predicting environmental fluxes. To investigate impacts of RN’s topology on transport processes, we introduce a systematic framework based on the concept of dynamic clusters, where the connectivity of subcatchments is assessed according to two complementary criteria: minimum‐ and maximum‐flow connectivity. Our analysis from simple synthetic RNs and several natural river basins across the United States reveals the key topological features underlying the efficiency of flux transport and aggregation. Namely, the timing of basin‐scale connectivity at low‐flow conditions is controlled by the abundance of topologically asymmetric junctions (side‐branching), which at the same time, result in a slow‐down of the flux convergence at the outlet (maximum‐flow). Our results, when compared with observed topological trends in RNs as a function of climate, indicate that humid basins exhibit topologies which are “naturally engineered” to slow‐down fluxes.

 

The Braiding Index (BI), defined as the average count of intercepted channels per cross‐section, is a widely used metric for characterizing multi‐thread river systems. However, it does not account for the diversity of channels (e.g., in terms of water discharge) within different cross‐sections, omitting important information related to system complexity. Here we present a modification ofBI,the Entropic Braiding Index (eBI), which augments the information content inBIby using Shannon Entropy to encode the diversity of channels in each cross section.eBIis interpreted as the number of “effective channels” per cross‐section, allowing a direct comparison with the traditionalBI. We demonstrate the potential of the ratioBI/eBIto quantify channel disparity, differentiate types of multi‐thread systems (braided vs. anastomosed), and assess the effect of discharge variability, such as seasonal flooding, on river cross‐section stability.

 

Understanding how thermokarst lakes on arctic river deltas will respond to rapid warming is critical for projecting how carbon storage and fluxes will change in those vulnerable environments. Yet, this understanding is currently limited partly due to the complexity of disentangling significant interannual variability from the longer‐term surface water signatures on the landscape, using the short summertime window of optical spaceborne observations. Here, we rigorously separate perennial lakes from ephemeral wetlands on 12 arctic deltas and report distinct size distributions and climate trends for the two waterbodies. Namely, we find a lognormal distribution for lakes and a power‐law distribution for wetlands, consistent with a simple proportionate growth model and inundated topography, respectively. Furthermore, while no trend with temperature is found for wetlands, a statistically significant decreasing trend of mean lake size with warmer temperatures is found, attributed to colder deltas having deeper and thicker permafrost preserving larger lakes.